Hypothesis & Investigation
state a hypothesis about a relationship between the following pair of variables:
temperature and crime rate
as T increases, crime rate increases
or
as T increases, crime rate decreases
A researcher chooses 50 students completely at random from a school. What type of sampling is this?
Random sampling
A data set records temperatures from 10°C to 25°C. You use the trend to predict the temperature at 20°C. What type of prediction is this?
Interpolation
A relation has a constant rate of change. Is it linear or non-linear?
linear
A survey asks 100 randomly selected students what their favourite school subject is. Why is random sampling useful?
It gives students an equal chance of being selected and can reduce bias.
Complete the hypothesis: “If the amount of sunlight increases, then a plant will ______.”
Grow more quickly/taller
A school surveys every 10th student entering the cafeteria. What type of sampling is this?
Systematic sampling
If the points generally fall from left to right, what type of correlation is shown?
Negative correlation
Is y=3x+5y=3x+5 a linear or non-linear relation?
linear
A distance-time graph shows a straight line rising from (0,0) to (4,20). What is the object's speed?
5 km/h
A student predicts that the number of hours of sleep affects students' test scores. Identify the independent variable.
Number of hours of sleep
A researcher divides students into Grades 9, 10, 11, and 12, then randomly chooses students from each grade. What type of sampling is this?
Stratified sampling
What is it called when you estimate a value outside the range of known data?
Extrapolation
Is y=x2+2y=x^2+2 a linear or non-linear relation?
non-linear
The relation y=2x+7 is used to predict yy when x=15, even though the original data only included xx-values from 1 to 10. Is this interpolation or extrapolation?
Extrapolation
A student investigates whether the amount of time spent exercising affects resting heart rate. What is the dependent variable?
Resting heart rate
A principal wants to know what the entire school thinks about a new uniform. She asks only the students in her Grade 9 math class. What is wrong with this sample?
It is a biased/convenience sample because it may not represent the entire school.
What is it called when you estimate a value between known data points?
Interpolation
On a distance-time graph, what does a horizontal line mean? what does slope mean?
distance
speed
A researcher surveys every 5th person who enters a shopping mall. What type of sampling is this?
Systematic sampling
A student proposes: “If students spend more time studying, then their test marks will increase.” What are the independent and dependent variables, and what relationship would you expect?
Independent: study time; Dependent: test mark; Expected relationship: positive trend.
identify type of sampling:
a. president of a restaurant chain interviews only employee's of one branch
b. student council selects a number of students from each class. the number is proportional to the size of class.
a. biased/non-random sampling
b. stratified sampling
A company's sales are recorded for years 2020–2025. A student uses the trend to predict sales for 2030. What type of prediction is this, and why is it generally less reliable than interpolation?
Extrapolation; it predicts outside the known data range, so the existing trend may not continue.
On a distance-time graph, a person's line is very steep from 0 to 5 minutes, then becomes less steep from 5 to 10 minutes. What does this tell you about the person's motion?
The person is moving faster during the first 5 minutes and slower during the next 5 minutes.
A school has 40% Grade 9 students, 30% Grade 10 students, 20% Grade 11 students, and 10% Grade 12 students. A researcher selects students from each grade in the same proportions. What type of sampling is this?
Stratified sampling